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A degree (in full, a degree of arc, arc degree, or arcdegree ), usually denoted by ° (the degree symbol ), is a measurement of a plane angle in which one full rotation is 360 degrees. [4] It is not an SI unit —the SI unit of angular measure is the radian —but it is mentioned in the SI brochure as an accepted unit. [5]
A minute of arc is π 10 800 of a radian . A second of arc, arcsecond (arcsec), or arc second, denoted by the symbol ″, [2] is 1 60 of an arcminute, 1 3600 of a degree, [1] 1 1 296 000 of a turn, and π 648 000 (about 1 206 264.8) of a radian. These units originated in Babylonian astronomy as sexagesimal (base 60) subdivisions of the degree ...
The second of arc (or arcsecond, or just second) is 1 / 60 of a minute of arc and 1 / 3600 of a degree (n = 1,296,000). It is denoted by a double prime ( ″ ). For example, 3° 7′ 30″ is equal to 3 + 7 / 60 + 30 / 3600 degrees, or 3.125 degrees. The arcsecond is the angle used to measure a parsec: grad: 400: 0°54′
30° and 60° The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.
The solid angle of a sphere measured from any point in its interior is 4 π sr, and the solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2 π /3 sr. Solid angles can also be measured in square degrees (1 sr = (180/ π) 2 square degrees), in square arc-minutes and square arc-seconds, or in fractions of ...
For equal permeabilities (e.g., non-magnetic media), if θ i and θ t are complementary, we can substitute sin θ t for cos θ i , and sin θ i for cos θ t , so that the numerator in equation becomes n 2 sin θ t − n 1 sin θ i , which is zero (by Snell's law).
The 13th CGPM also held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction 1 / 273.16 of the thermodynamic temperature of the triple point of water." [4] [42] [43]
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse ), and the cosine is ...